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Fifth Edition,last update October 18,20062Lessons In Electric Circuits,Volume I { DCBy Tony R.KuphaldtFifth Edition,last update October 18,2006ic°2000-2006,Tony R.KuphaldtThis book is published under the terms and conditions of the Design Science License.Theseterms and conditions allow for free copying,distribution,and/or modi¯cation of this document bythe general public.The full Design Science License text is included in the last chapter.As an open and collaboratively developed text,this book is distributed in the hope that itwill be useful,but WITHOUT ANY WARRANTY;without even the implied warranty of MER-CHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.See the Design Science Licensefor more details.Available in its entirety as part of the Open Book Project collection at:www.ibiblio.org/obp/electricCircuitsPRINTING HISTORY² First Edition:Printed in June of 2000.Plain-ASCII illustrations for universal computerreadability.² Second Edition:Printed in September of 2000.Illustrations reworked in standard graphic(eps and jpeg) format.Source ¯les translated to Texinfo format for easy online and printedpublication.² Third Edition:Equations and tables reworked as graphic images rather than plain-ASCII text.² Fourth Edition:Printed in August 2001.Source ¯les translated to SubML format.SubML isa simple markup language designed to easily convert to other markups like LATEX,HTML,orDocBook using nothing but search-and-replace substitutions.² Fifth Edition:Printed in August 2002.New sections added,and error corrections made,sincethe fourth edition.iiContents1 BASIC CONCEPTS OF ELECTRICITYix1.1 Static electricity......................................ix1.2 Conductors,insulators,and electron °ow........................xv1.3 Electric circuits......................................xix1.4 Voltage and current....................................xxi1.5 Resistance.........................................xxx1.6 Voltage and current in a practical circuit........................xxxiv1.7 Conventional versus electron °ow............................xxxv1.8 Contributors........................................xxxix2 OHM's LAWxli2.1 How voltage,current,and resistance relate.......................xli2.2 An analogy for Ohm's Law................................xlvi2.3 Power in electric circuits.................................xlvii2.4 Calculating electric power.................................xlix2.5 Resistors..........................................lii2.6 Nonlinear conduction...................................lvii2.7 Circuit wiring.......................................lxii2.8 Polarity of voltage drops.................................lxvi2.9 Computer simulation of electric circuits.........................lxvii2.10 Contributors........................................lxxxi3 ELECTRICAL SAFETYlxxxiii3.1 The importance of electrical safety............................lxxxiii3.2 Physiological e®ects of electricity.............................lxxxiv3.3 Shock current path....................................lxxxvi3.4 Ohm's Law (again!)....................................xci3.5 Safe practices.......................................xcviii3.6 Emergency response....................................cii3.7 Common sources of hazard................................ciii3.8 Safe circuit design.....................................cvi3.9 Safe meter usage......................................cxi3.10 Electric shock data....................................cxxi3.11 Contributors........................................cxxiiiiiv CONTENTS4 SCIENTIFIC NOTATION AND METRIC PREFIXEScxxiii4.1 Scienti¯c notation.....................................cxxiii4.2 Arithmetic with scienti¯c notation............................cxxv4.3 Metric notation......................................cxxvii4.4 Metric pre¯x conversions.................................cxxviii4.5 Hand calculator use....................................cxxix4.6 Scienti¯c notation in SPICE...............................cxxx4.7 Contributors........................................cxxxii5 SERIES AND PARALLEL CIRCUITScxxxiii5.1 What are"series"and"parallel"circuits?........................cxxxiii5.2 Simple series circuits...................................cxxxvi5.3 Simple parallel circuits..................................cxlii5.4 Conductance........................................cxlvii5.5 Power calculations.....................................cxlix5.6 Correct use of Ohm's Law................................cl5.7 Component failure analysis................................clii5.8 Building simple resistor circuits.............................clviii5.9 Contributors........................................clxxiii6 DIVIDER CIRCUITS AND KIRCHHOFF'S LAWSclxxv6.1 Voltage divider circuits..................................clxxv6.2 Kirchho®'s Voltage Law (KVL).............................clxxxiii6.3 Current divider circuits..................................cxciii6.4 Kirchho®'s Current Law (KCL).............................cxcvii6.5 Contributors........................................cxcix7 SERIES-PARALLEL COMBINATION CIRCUITScci7.1 What is a series-parallel circuit?.............................cci7.2 Analysis technique.....................................cciv7.3 Re-drawing complex schematics.............................ccxi7.4 Component failure analysis................................ccxix7.5 Building series-parallel resistor circuits.........................ccxxiv7.6 Contributors........................................ccxxxvi8 DC METERING CIRCUITSccxxxix8.1 What is a meter?.....................................ccxxxix8.2 Voltmeter design......................................ccxliv8.3 Voltmeter impact on measured circuit..........................ccxlix8.4 Ammeter design......................................cclvii8.5 Ammeter impact on measured circuit..........................cclxiii8.6 Ohmmeter design.....................................cclxvii8.7 High voltage ohmmeters.................................cclxxi8.8 Multimeters........................................cclxxix8.9 Kelvin (4-wire) resistance measurement.........................cclxxxiv8.10 Bridge circuits.......................................cclxxxixCONTENTS v8.11 Wattmeter design.....................................ccxcvi8.12 Creating custom calibration resistances.........................ccxcviii8.13 Contributors........................................ccc9 ELECTRICAL INSTRUMENTATION SIGNALSccci9.1 Analog and digital signals.................................ccci9.2 Voltage signal systems...................................ccciv9.3 Current signal systems..................................cccv9.4 Tachogenerators......................................cccviii9.5 Thermocouples.......................................cccix9.6 pH measurement......................................cccxiv9.7 Strain gauges........................................cccxx9.8 Contributors........................................cccxxvii10 DC NETWORK ANALYSIScccxxix10.1 What is network analysis?................................cccxxix10.2 Branch current method..................................cccxxxii10.3 Mesh current method...................................cccxl10.4 Node voltage method...................................ccclvi10.5 Introduction to network theorems............................ccclx10.6 Millman's Theorem....................................ccclx10.7 Superposition Theorem..................................ccclxiii10.8 Thevenin's Theorem....................................ccclxviii10.9 Norton's Theorem.....................................ccclxxii10.10 Thevenin-Norton equivalencies..............................ccclxxvi10.11 Millman's Theorem revisited...............................ccclxxviii10.12 Maximum Power Transfer Theorem...........................ccclxxx10.13 ¢-Y and Y-¢ conversions.................................ccclxxxii10.14 Contributors........................................ccclxxxviii11 BATTERIES AND POWER SYSTEMSccclxxxix11.1 Electron activity in chemical reactions..........................ccclxxxix11.2 Battery construction....................................cccxcv11.3 Battery ratings.......................................cccxcviii11.4 Special-purpose batteries.................................cd11.5 Practical considerations..................................cdiv11.6 Contributors........................................cdvi12 PHYSICS OF CONDUCTORS AND INSULATORScdvii12.1 Introduction........................................cdvii12.2 Conductor size.......................................cdix12.3 Conductor ampacity....................................cdxv12.4 Fuses............................................cdxvii12.5 Speci¯c resistance.....................................cdxxiv12.6 Temperature coe±cient of resistance...........................cdxxviii12.7 Superconductivity.....................................cdxxxivi CONTENTS12.8 Insulator breakdown voltage...............................cdxxxiv12.9 Data............................................cdxxxv12.10 Contributors........................................cdxxxv13 CAPACITORScdxxxvii13.1 Electric ¯elds and capacitance..............................cdxxxvii13.2 Capacitors and calculus..................................cdxli13.3 Factors a®ecting capacitance...............................cdxlvii13.4 Series and parallel capacitors...............................cdl13.5 Practical considerations..................................cdli13.6 Contributors........................................cdlvi14 MAGNETISM AND ELECTROMAGNETISMcdlvii14.1 Permanent magnets....................................cdlvii14.2 Electromagnetism.....................................cdlxi14.3 Magnetic units of measurement.............................cdlxiii14.4 Permeability and saturation...............................cdlxvi14.5 Electromagnetic induction................................cdlxxi14.6 Mutual inductance.....................................cdlxxiii14.7 Contributors........................................cdlxxv15 INDUCTORScdlxxvii15.1 Magnetic ¯elds and inductance..............................cdlxxvii15.2 Inductors and calculus..................................cdlxxxi15.3 Factors a®ecting inductance...............................cdlxxxvii15.4 Series and parallel inductors...............................cdxcii15.5 Practical considerations..................................cdxciv15.6 Contributors........................................cdxciv16 RC AND L/R TIME CONSTANTScdxcv16.1 Electrical transients....................................cdxcv16.2 Capacitor transient response...............................cdxcv16.3 Inductor transient response................................cdxcviii16.4 Voltage and current calculations.............................di16.5 Why L/R and not LR?..................................dvii16.6 Complex voltage and current calculations........................dix16.7 Complex circuits......................................dxi16.8 Solving for unknown time.................................dxvi16.9 Contributors........................................dxviiiBIBLIOGRAPHYdxixA-1 ABOUT THIS BOOKdxxiA-2 CONTRIBUTOR LISTdxxvA-3 DESIGN SCIENCE LICENSEdxxxiCONTENTS viiINDEXdxxxivviii CONTENTSChapter 1BASIC CONCEPTS OFELECTRICITYContents1.1 Static electricity................................ix1.2 Conductors,insulators,and electron °ow................xv1.3 Electric circuits................................xix1.4 Voltage and current.............................xxi1.5 Resistance...................................xxx1.6 Voltage and current in a practical circuit................xxxiv1.7 Conventional versus electron °ow.....................xxxv1.8 Contributors..................................xxxix1.1 Static electricityIt was discovered centuries ago that certain types of materials would mysteriously attract one anotherafter being rubbed together.For example:after rubbing a piece of silk against a piece of glass,thesilk and glass would tend to stick together.Indeed,there was an attractive force that could bedemonstrated even when the two materials were separated:Glass rod Silk clothattractionixx CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYGlass and silk aren't the only materials known to behave like this.Anyone who has ever brushedup against a latex balloon only to ¯nd that it tries to stick to them has experienced this same phe-nomenon.Para±n wax and wool cloth are another pair of materials early experimenters recognizedas manifesting attractive forces after being rubbed together:attractionWool clothWaxThis phenomenon became even more interesting when it was discovered that identical materials,after having been rubbed with their respective cloths,always repelled each other:Glass rodGlass rodrepulsionWaxrepulsionWaxIt was also noted that when a piece of glass rubbed with silk was exposed to a piece of waxrubbed with wool,the two materials would attract one another:1.1.STATIC ELECTRICITY xiGlass rodWaxattractionFurthermore,it was found that any material demonstrating properties of attraction or repulsionafter being rubbed could be classed into one of two distinct categories:attracted to glass and repelledby wax,or repelled by glass and attracted to wax.It was either one or the other:there were nomaterials found that would be attracted to or repelled by both glass and wax,or that reacted toone without reacting to the other.More attention was directed toward the pieces of cloth used to do the rubbing.It was discoveredthat after rubbing two pieces of glass with two pieces of silk cloth,not only did the glass pieces repeleach other,but so did the cloths.The same phenomenon held for the pieces of wool used to rub thewax:Silk clothSilk clothrepulsionrepulsionWool cloth Wool clothNow,this was really strange to witness.After all,none of these objects were visibly altered bythe rubbing,yet they de¯nitely behaved di®erently than before they were rubbed.Whatever changetook place to make these materials attract or repel one another was invisible.Some experimenters speculated that invisible"°uids"were being transferred from one object toanother during the process of rubbing,and that these"°uids"were able to e®ect a physical forcexii CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYover a distance.Charles Dufay was one the early experimenters who demonstrated that there werede¯nitely two di®erent types of changes wrought by rubbing certain pairs of objects together.Thefact that there was more than one type of change manifested in these materials was evident by thefact that there were two types of forces produced:attraction and repulsion.The hypothetical °uidtransfer became known as a charge.One pioneering researcher,Benjamin Franklin,came to the conclusion that there was only one°uid exchanged between rubbed objects,and that the two di®erent"charges"were nothing morethan either an excess or a de¯ciency of that one °uid.After experimenting with wax and wool,Franklin suggested that the coarse wool removed some of this invisible °uid from the smooth wax,causing an excess of °uid on the wool and a de¯ciency of °uid on the wax.The resulting disparityin °uid content between the wool and wax would then cause an attractive force,as the °uid triedto regain its former balance between the two materials.Postulating the existence of a single"°uid"that was either gained or lost through rubbingaccounted best for the observed behavior:that all these materials fell neatly into one of two categorieswhen rubbed,and most importantly,that the two active materials rubbed against each other alwaysfell into opposing categories as evidenced by their invariable attraction to one another.In otherwords,there was never a time where two materials rubbed against each other both became eitherpositive or negative.Following Franklin's speculation of the wool rubbing something o® of the wax,the type of chargethat was associated with rubbed wax became known as"negative"(because it was supposed to havea de¯ciency of °uid) while the type of charge associated with the rubbing wool became known as"positive"(because it was supposed to have an excess of °uid).Little did he know that his innocentconjecture would cause much confusion for students of electricity in the future!Precise measurements of electrical charge were carried out by the French physicist CharlesCoulomb in the 1780's using a device called a torsional balance measuring the force generatedbetween two electrically charged objects.The results of Coulomb's work led to the development ofa unit of electrical charge named in his honor,the coulomb.If two"point"objects (hypotheticalobjects having no appreciable surface area) were equally charged to a measure of 1 coulomb,andplaced 1 meter (approximately 1 yard) apart,they would generate a force of about 9 billion newtons(approximately 2 billion pounds),either attracting or repelling depending on the types of chargesinvolved.It was discovered much later that this"°uid"was actually composed of extremely small bits ofmatter called electrons,so named in honor of the ancient Greek word for amber:another materialexhibiting charged properties when rubbed with cloth.Experimentation has since revealed that allobjects are composed of extremely small"building-blocks"known as atoms,and that these atomsare in turn composed of smaller components known as particles.The three fundamental particlescomprising atoms are called protons,neutrons,and electrons.Atoms are far too small to be seen,but if we could look at one,it might appear something like this:1.1.STATIC ELECTRICITY xiiiNNNNNNPPPPPPeee eeeeNP= electron= proton= neutronEven though each atom in a piece of material tends to hold together as a unit,there's actuallya lot of empty space between the electrons and the cluster of protons and neutrons residing in themiddle.This crude model is that of the element carbon,with six protons,six neutrons,and six electrons.In any atom,the protons and neutrons are very tightly bound together,which is an importantquality.The tightly-bound clump of protons and neutrons in the center of the atom is called thenucleus,and the number of protons in an atom's nucleus determines its elemental identity:changethe number of protons in an atom's nucleus,and you change the type of atom that it is.In fact,if you could remove three protons from the nucleus of an atom of lead,you will have achieved theold alchemists'dream of producing an atom of gold!The tight binding of protons in the nucleusis responsible for the stable identity of chemical elements,and the failure of alchemists to achievetheir dream.Neutrons are much less in°uential on the chemical character and identity of an atomthan protons,although they are just as hard to add to or remove from the nucleus,being so tightly bound.Ifneutrons are added or gained,the atom will still retain the same chemical identity,but its mass willchange slightly and it may acquire strange nuclear properties such as radioactivity.However,electrons have signi¯cantly more freedom to move around in an atom than eitherprotons or neutrons.In fact,they can be knocked out of their respective positions (even leaving theatom entirely!) by far less energy than what it takes to dislodge particles in the nucleus.If thishappens,the atom still retains its chemical identity,but an important imbalance occurs.Electronsand protons are unique in the fact that they are attracted to one another over a distance.It is thisattraction over distance which causes the attraction between rubbed objects,where electrons aremoved away from their original atoms to reside around atoms of another object.Electrons tend to repel other electrons over a distance,as do protons with other protons.Theonly reason protons bind together in the nucleus of an atom is because of a much stronger forcexiv CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYcalled the strong nuclear force which has e®ect only under very short distances.Because of thisattraction/repulsion behavior between individual particles,electrons and protons are said to haveopposite electric charges.That is,each electron has a negative charge,and each proton a positivecharge.In equal numbers within an atom,they counteract each other's presence so that the netcharge within the atomis zero.This is why the picture of a carbon atomhad six electrons:to balanceout the electric charge of the six protons in the nucleus.If electrons leave or extra electrons arrive,the atom's net electric charge will be imbalanced,leaving the atom"charged"as a whole,causing itto interact with charged particles and other charged atoms nearby.Neutrons are neither attractedto or repelled by electrons,protons,or even other neutrons,and are consequently categorized ashaving no charge at all.The process of electrons arriving or leaving is exactly what happens when certain combinationsof materials are rubbed together:electrons from the atoms of one material are forced by the rubbingto leave their respective atoms and transfer over to the atoms of the other material.In other words,electrons comprise the"°uid"hypothesized by Benjamin Franklin.The operational de¯nition of acoulomb as the unit of electrical charge (in terms of force generated between point charges) wasfound to be equal to an excess or de¯ciency of about 6,250,000,000,000,000,000 electrons.Or,statedin reverse terms,one electron has a charge of about 0.00000000000000000016 coulombs.Being thatone electron is the smallest known carrier of electric charge,this last ¯gure of charge for the electronis de¯ned as the elementary charge.The result of an imbalance of this"°uid"(electrons) between objects is called static electricity.It is called"static"because the displaced electrons tend to remain stationary after being movedfrom one material to another.In the case of wax and wool,it was determined through furtherexperimentation that electrons in the wool actually transferred to the atoms in the wax,which isexactly opposite of Franklin's conjecture!In honor of Franklin's designation of the wax's chargebeing"negative"and the wool's charge being"positive,"electrons are said to have a"negative"charging in°uence.Thus,an object whose atoms have received a surplus of electrons is said to benegatively charged,while an object whose atoms are lacking electrons is said to be positively charged,as confusing as these designations may seem.By the time the true nature of electric"°uid"wasdiscovered,Franklin's nomenclature of electric charge was too well established to be easily changed,and so it remains to this day.² REVIEW:² All materials are made up of tiny"building blocks"known as atoms.² All atoms contain particles called electrons,protons,and neutrons.² Electrons have a negative (-) electric charge.² Protons have a positive (+) electric charge.² Neutrons have no electric charge.² Electrons can be dislodged from atoms much easier than protons or neutrons.² The number of protons in an atom's nucleus determines its identity as a unique element.1.2.CONDUCTORS,INSULATORS,AND ELECTRON FLOW xv1.2 Conductors,insulators,and electron °owThe electrons of di®erent types of atoms have di®erent degrees of freedom to move around.Withsome types of materials,such as metals,the outermost electrons in the atoms are so loosely boundthat they chaotically move in the space between the atoms of that material by nothing more thanthe in°uence of room-temperature heat energy.Because these virtually unbound electrons are freeto leave their respective atoms and °oat around in the space between adjacent atoms,they are oftencalled free electrons.In other types of materials such as glass,the atoms'electrons have very little freedom to movearound.While external forces such as physical rubbing can force some of these electrons to leavetheir respective atoms and transfer to the atoms of another material,they do not move betweenatoms within that material very easily.This relative mobility of electrons within a material is known as electric conductivity.Conduc-tivity is determined by the types of atoms in a material (the number of protons in each atom'snucleus,determining its chemical identity) and how the atoms are linked together with one another.Materials with high electron mobility (many free electrons) are called conductors,while materialswith low electron mobility (few or no free electrons) are called insulators.Here are a few common examples of conductors and insulators:² Conductors:² silver² copper² gold² aluminum² iron² steel² brass² bronze² mercury² graphite² dirty water² concrete² Insulators:² glassxvi CHAPTER 1.BASIC CONCEPTS OF ELECTRICITY² rubber² oil² asphalt² ¯berglass² porcelain² ceramic² quartz² (dry) cotton² (dry) paper² (dry) wood² plastic² air² diamond² pure waterIt must be understood that not all conductive materials have the same level of conductivity,and not all insulators are equally resistant to electron motion.Electrical conductivity is analogousto the transparency of certain materials to light:materials that easily"conduct"light are called"transparent,"while those that don't are called"opaque."However,not all transparent materialsare equally conductive to light.Window glass is better than most plastics,and certainly better than"clear"¯berglass.So it is with electrical conductors,some being better than others.For instance,silver is the best conductor in the"conductors"list,o®ering easier passage forelectrons than any other material cited.Dirty water and concrete are also listed as conductors,butthese materials are substantially less conductive than any metal.Physical dimension also impacts conductivity.For instance,if we take two strips of the sameconductive material { one thin and the other thick { the thick strip will prove to be a better conductorthan the thin for the same length.If we take another pair of strips { this time both with the samethickness but one shorter than the other { the shorter one will o®er easier passage to electrons thanthe long one.This is analogous to water °ow in a pipe:a fat pipe o®ers easier passage than a skinnypipe,and a short pipe is easier for water to move through than a long pipe,all other dimensionsbeing equal.It should also be understood that some materials experience changes in their electrical propertiesunder di®erent conditions.Glass,for instance,is a very good insulator at room temperature,butbecomes a conductor when heated to a very high temperature.Gases such as air,normally insulatingmaterials,also become conductive if heated to very high temperatures.Most metals become poorerconductors when heated,and better conductors when cooled.Many conductive materials becomeperfectly conductive (this is called superconductivity) at extremely low temperatures.1.2.CONDUCTORS,INSULATORS,AND ELECTRON FLOW xviiWhile the normal motion of"free"electrons in a conductor is random,with no particular direc-tion or speed,electrons can be in°uenced to move in a coordinated fashion through a conductivematerial.This uniform motion of electrons is what we call electricity,or electric current.To bemore precise,it could be called dynamic electricity in contrast to static electricity,which is an un-moving accumulation of electric charge.Just like water °owing through the emptiness of a pipe,electrons are able to move within the empty space within and between the atoms of a conductor.The conductor may appear to be solid to our eyes,but any material composed of atoms is mostlyempty space!The liquid-°ow analogy is so ¯tting that the motion of electrons through a conductoris often referred to as a"°ow."A noteworthy observation may be made here.As each electron moves uniformly through aconductor,it pushes on the one ahead of it,such that all the electrons move together as a group.The starting and stopping of electron °ow through the length of a conductive path is virtuallyinstantaneous from one end of a conductor to the other,even though the motion of each electronmay be very slow.An approximate analogy is that of a tube ¯lled end-to-end with marbles:TubeMarble MarbleThe tube is full of marbles,just as a conductor is full of free electrons ready to be moved by anoutside in°uence.If a single marble is suddenly inserted into this full tube on the left-hand side,another marble will immediately try to exit the tube on the right.Even though each marble onlytraveled a short distance,the transfer of motion through the tube is virtually instantaneous fromthe left end to the right end,no matter how long the tube is.With electricity,the overall e®ectfrom one end of a conductor to the other happens at the speed of light:a swift 186,000 miles persecond!!!Each individual electron,though,travels through the conductor at a much slower pace.If we want electrons to °ow in a certain direction to a certain place,we must provide the properpath for them to move,just as a plumber must install piping to get water to °ow where he or shewants it to °ow.To facilitate this,wires are made of highly conductive metals such as copper oraluminum in a wide variety of sizes.Remember that electrons can °ow only when they have the opportunity to move in the spacebetween the atoms of a material.This means that there can be electric current only where thereexists a continuous path of conductive material providing a conduit for electrons to travel through.Inthe marble analogy,marbles can °ow into the left-hand side of the tube (and,consequently,throughthe tube) if and only if the tube is open on the right-hand side for marbles to °ow out.If the tubeis blocked on the right-hand side,the marbles will just"pile up"inside the tube,and marble"°ow"will not occur.The same holds true for electric current:the continuous °ow of electrons requiresthere be an unbroken path to permit that °ow.Let's look at a diagram to illustrate how this works:A thin,solid line (as shown above) is the conventional symbol for a continuous piece of wire.Since the wire is made of a conductive material,such as copper,its constituent atoms have manyfree electrons which can easily move through the wire.However,there will never be a continuous oruniform °ow of electrons within this wire unless they have a place to come from and a place to go.Let's add an hypothetical electron"Source"and"Destination:"Electron ElectronSource DestinationNow,with the Electron Source pushing new electrons into the wire on the left-hand side,electronxviii CHAPTER 1.BASIC CONCEPTS OF ELECTRICITY°ow through the wire can occur (as indicated by the arrows pointing from left to right).However,the °ow will be interrupted if the conductive path formed by the wire is broken:Electron ElectronSource Destinationno flow!no flow!(break)Since air is an insulating material,and an air gap separates the two pieces of wire,the once-continuous path has now been broken,and electrons cannot °ow from Source to Destination.Thisis like cutting a water pipe in two and capping o® the broken ends of the pipe:water can't °ow ifthere's no exit out of the pipe.In electrical terms,we had a condition of electrical continuity whenthe wire was in one piece,and now that continuity is broken with the wire cut and separated.If we were to take another piece of wire leading to the Destination and simply make physicalcontact with the wire leading to the Source,we would once again have a continuous path for electronsto °ow.The two dots in the diagram indicate physical (metal-to-metal) contact between the wirepieces:Electron ElectronSource Destinationno flow!(break)Now,we have continuity from the Source,to the newly-made connection,down,to the right,andup to the Destination.This is analogous to putting a"tee"¯tting in one of the capped-o® pipes anddirecting water through a new segment of pipe to its destination.Please take note that the brokensegment of wire on the right hand side has no electrons °owing through it,because it is no longerpart of a complete path from Source to Destination.It is interesting to note that no"wear"occurs within wires due to this electric current,unlikewater-carrying pipes which are eventually corroded and worn by prolonged °ows.Electrons doencounter some degree of friction as they move,however,and this friction can generate heat in aconductor.This is a topic we'll explore in much greater detail later.² REVIEW:² In conductive materials,the outer electrons in each atom can easily come or go,and are calledfree electrons.² In insulating materials,the outer electrons are not so free to move.² All metals are electrically conductive.² Dynamic electricity,or electric current,is the uniformmotion of electrons through a conductor.Static electricity is an unmoving,accumulated charge formed by either an excess or de¯ciencyof electrons in an object.² For electrons to °ow continuously (inde¯nitely) through a conductor,there must be a complete,unbroken path for them to move both into and out of that conductor.1.3.ELECTRIC CIRCUITS xix1.3 Electric circuitsYou might have been wondering how electrons can continuously °ow in a uniform direction throughwires without the bene¯t of these hypothetical electron Sources and Destinations.In order for theSource-and-Destination scheme to work,both would have to have an in¯nite capacity for electronsin order to sustain a continuous °ow!Using the marble-and-tube analogy,the marble source andmarble destination buckets would have to be in¯nitely large to contain enough marble capacity fora"°ow"of marbles to be sustained.The answer to this paradox is found in the concept of a circuit:a never-ending looped pathwayfor electrons.If we take a wire,or many wires joined end-to-end,and loop it around so that it formsa continuous pathway,we have the means to support a uniform °ow of electrons without having toresort to in¯nite Sources and Destinations:electrons can flowin a path withoutbeginning or end,continuing forever!A marble-and-hula-hoop "circuit"Each electron advancing clockwise in this circuit pushes on the one in front of it,which pusheson the one in front of it,and so on,and so on,just like a hula-hoop ¯lled with marbles.Now,wehave the capability of supporting a continuous °ow of electrons inde¯nitely without the need forin¯nite electron supplies and dumps.All we need to maintain this °ow is a continuous means ofmotivation for those electrons,which we'll address in the next section of this chapter.It must be realized that continuity is just as important in a circuit as it is in a straight pieceof wire.Just as in the example with the straight piece of wire between the electron Source andDestination,any break in this circuit will prevent electrons from °owing through it:xx CHAPTER 1.BASIC CONCEPTS OF ELECTRICITY(break)electron flow cannotin a "broken" circuit!no flow!no flow!no flow!occur anywherecontinuousAn important principle to realize here is that it doesn't matter where the break occurs.Anydiscontinuity in the circuit will prevent electron °ow throughout the entire circuit.Unless there isa continuous,unbroken loop of conductive material for electrons to °ow through,a sustained °owsimply cannot be maintained.electron flow cannotin a "broken" circuit!no flow!no flow!no flow!(break)occur anywherecontinuous² REVIEW:² A circuit is an unbroken loop of conductive material that allows electrons to °ow throughcontinuously without beginning or end.² If a circuit is"broken,"that means it's conductive elements no longer form a complete path,and continuous electron °ow cannot occur in it.² The location of a break in a circuit is irrelevant to its inability to sustain continuous electron°ow.Any break,anywhere in a circuit prevents electron °ow throughout the circuit.1.4.VOLTAGE AND CURRENT xxi1.4 Voltage and currentAs was previously mentioned,we need more than just a continuous path (circuit) before a continuous°ow of electrons will occur:we also need some means to push these electrons around the circuit.Just like marbles in a tube or water in a pipe,it takes some kind of in°uencing force to initiate °ow.With electrons,this force is the same force at work in static electricity:the force produced by animbalance of electric charge.If we take the examples of wax and wool which have been rubbed together,we ¯nd that thesurplus of electrons in the wax (negative charge) and the de¯cit of electrons in the wool (positivecharge) creates an imbalance of charge between them.This imbalance manifests itself as an attractiveforce between the two objects:attractionWool clothWax---- ------- -------------------- -+ ++++++++++++++++++++++++++++++++++++ ++++++If a conductive wire is placed between the charged wax and wool,electrons will °ow through it,as some of the excess electrons in the wax rush through the wire to get back to the wool,¯lling thede¯ciency of electrons there:Wool clothWax-------- -----------+ + ++++++++++++++++++++++ ++++wire- - -electron flowThe imbalance of electrons between the atoms in the wax and the atoms in the wool creates aforce between the two materials.With no path for electrons to °ow from the wax to the wool,allthis force can do is attract the two objects together.Now that a conductor bridges the insulatinggap,however,the force will provoke electrons to °ow in a uniform direction through the wire,ifonly momentarily,until the charge in that area neutralizes and the force between the wax and wooldiminishes.The electric charge formed between these two materials by rubbing them together serves to storea certain amount of energy.This energy is not unlike the energy stored in a high reservoir of waterthat has been pumped from a lower-level pond:xxii CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYPumpPondReservoirEnergy storedWater flowThe in°uence of gravity on the water in the reservoir creates a force that attempts to move thewater down to the lower level again.If a suitable pipe is run from the reservoir back to the pond,water will °ow under the in°uence of gravity down from the reservoir,through the pipe:PondReservoirEnergy releasedIt takes energy to pump that water from the low-level pond to the high-level reservoir,and themovement of water through the piping back down to its original level constitutes a releasing ofenergy stored from previous pumping.1.4.VOLTAGE AND CURRENT xxiiiIf the water is pumped to an even higher level,it will take even more energy to do so,thus moreenergy will be stored,and more energy released if the water is allowed to °ow through a pipe backdown again:ReservoirPumpPondEnergy storedMore energy releasedMore energy storedEnergy releasedReservoirPondPumpElectrons are not much di®erent.If we rub wax and wool together,we"pump"electrons awayfrom their normal"levels,"creating a condition where a force exists between the wax and wool,asxxiv CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYthe electrons seek to re-establish their former positions (and balance within their respective atoms).The force attracting electrons back to their original positions around the positive nuclei of theiratoms is analogous to the force gravity exerts on water in the reservoir,trying to draw it down toits former level.Just as the pumping of water to a higher level results in energy being stored,"pumping"electronsto create an electric charge imbalance results in a certain amount of energy being stored in thatimbalance.And,just as providing a way for water to °ow back down fromthe heights of the reservoirresults in a release of that stored energy,providing a way for electrons to °ow back to their original"levels"results in a release of stored energy.:registersWhen the electrons are poised in that static condition (just like water sitting still,high in areservoir),the energy stored there is called potential energy,because it has the possibility (potential)of release that has not been fully realized yet.When you scu® your rubber-soled shoes against afabric carpet on a dry day,you create an imbalance of electric charge between yourself and thecarpet.The action of scu±ng your feet stores energy in the form of an imbalance of electrons forcedfrom their original locations.This charge (static electricity) is stationary,and you won't realize thatenergy is being stored at all.However,once you place your hand against a metal doorknob (withlots of electron mobility to neutralize your electric charge),that stored energy will be released in theform of a sudden °ow of electrons through your hand,and you will perceive it as an electric shock!This potential energy,stored in the formof an electric charge imbalance and capable of provokingelectrons to °ow through a conductor,can be expressed as a term called voltage,which technically isa measure of potential energy per unit charge of electrons,or something a physicist would call speci¯cpotential energy.De¯ned in the context of static electricity,voltage is the measure of work requiredto move a unit charge from one location to another,against the force which tries to keep electriccharges balanced.In the context of electrical power sources,voltage is the amount of potentialenergy available (work to be done) per unit charge,to move electrons through a conductor.Because voltage is an expression of potential energy,representing the possibility or potential forenergy release as the electrons move from one"level"to another,it is always referenced betweentwo points.Consider the water reservoir analogy:1.4.VOLTAGE AND CURRENT xxvReservoirLocation #1Location #2DropDropBecause of the di®erence in the height of the drop,there's potential for much more energy to bereleased from the reservoir through the piping to location 2 than to location 1.The principle can beintuitively understood in dropping a rock:which results in a more violent impact,a rock droppedfrom a height of one foot,or the same rock dropped from a height of one mile?Obviously,the dropof greater height results in greater energy released (a more violent impact).We cannot assess theamount of stored energy in a water reservoir simply by measuring the volume of water any morethan we can predict the severity of a falling rock's impact simply from knowing the weight of therock:in both cases we must also consider how far these masses will drop from their initial height.The amount of energy released by allowing a mass to drop is relative to the distance between itsstarting and ending points.Likewise,the potential energy available for moving electrons from onepoint to another is relative to those two points.Therefore,voltage is always expressed as a quantitybetween two points.Interestingly enough,the analogy of a mass potentially"dropping"from oneheight to another is such an apt model that voltage between two points is sometimes called a voltagedrop.Voltage can be generated by means other than rubbing certain types of materials against eachother.Chemical reactions,radiant energy,and the in°uence of magnetism on conductors are a fewways in which voltage may be produced.Respective examples of these three sources of voltageare batteries,solar cells,and generators (such as the"alternator"unit under the hood of yourautomobile).For now,we won't go into detail as to how each of these voltage sources works { moreimportant is that we understand how voltage sources can be applied to create electron °ow in acircuit.Let's take the symbol for a chemical battery and build a circuit step by step:xxvi CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYBattery-+12Any source of voltage,including batteries,have two points for electrical contact.In this case,we have point 1 and point 2 in the above diagram.The horizontal lines of varying length indicatethat this is a battery,and they further indicate the direction which this battery's voltage will tryto push electrons through a circuit.The fact that the horizontal lines in the battery symbol appearseparated (and thus unable to serve as a path for electrons to move) is no cause for concern:in reallife,those horizontal lines represent metallic plates immersed in a liquid or semi-solid material thatnot only conducts electrons,but also generates the voltage to push them along by interacting withthe plates.Notice the little"+"and"-"signs to the immediate left of the battery symbol.The negative(-) end of the battery is always the end with the shortest dash,and the positive (+) end of thebattery is always the end with the longest dash.Since we have decided to call electrons"negatively"charged (thanks,Ben!),the negative end of a battery is that end which tries to push electrons outof it.Likewise,the positive end is that end which tries to attract electrons.With the"+"and"-"ends of the battery not connected to anything,there will be voltagebetween those two points,but there will be no °ow of electrons through the battery,because thereis no continuous path for the electrons to move.Battery-+12No flowPumpPondReservoirNo flow (once thereservoir has beencompletely filled)Electric BatteryWater analogyThe same principle holds true for the water reservoir and pump analogy:without a return pipeback to the pond,stored energy in the reservoir cannot be released in the form of water °ow.Once1.4.VOLTAGE AND CURRENT xxviithe reservoir is completely ¯lled up,no °ow can occur,no matter how much pressure the pumpmay generate.There needs to be a complete path (circuit) for water to °ow from the pond,to thereservoir,and back to the pond in order for continuous °ow to occur.We can provide such a path for the battery by connecting a piece of wire from one end of thebattery to the other.Forming a circuit with a loop of wire,we will initiate a continuous °ow ofelectrons in a clockwise direction:Battery-+12PumpPondReservoirWater analogywater flow!electron flow!water flow!Electric CircuitSo long as the battery continues to produce voltage and the continuity of the electrical pathisn't broken,electrons will continue to °ow in the circuit.Following the metaphor of water movingxxviii CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYthrough a pipe,this continuous,uniform °ow of electrons through the circuit is called a current.Solong as the voltage source keeps"pushing"in the same direction,the electron °ow will continue tomove in the same direction in the circuit.This single-direction °ow of electrons is called a DirectCurrent,or DC.In the second volume of this book series,electric circuits are explored where thedirection of current switches back and forth:Alternating Current,or AC.But for now,we'll justconcern ourselves with DC circuits.Because electric current is composed of individual electrons °owing in unison through a conductorby moving along and pushing on the electrons ahead,just like marbles through a tube or waterthrough a pipe,the amount of °ow throughout a single circuit will be the same at any point.If wewere to monitor a cross-section of the wire in a single circuit,counting the electrons °owing by,wewould notice the exact same quantity per unit of time as in any other part of the circuit,regardlessof conductor length or conductor diameter.If we break the circuit's continuity at any point,the electric current will cease in the entire loop,and the full voltage produced by the battery will be manifested across the break,between the wireends that used to be connected:Battery-+12(break)no flow!no flow!-+voltagedropNotice the"+"and"-"signs drawn at the ends of the break in the circuit,and how theycorrespond to the"+"and"-"signs next to the battery's terminals.These markers indicate thedirection that the voltage attempts to push electron °ow,that potential direction commonly referredto as polarity.Remember that voltage is always relative between two points.Because of this fact,the polarity of a voltage drop is also relative between two points:whether a point in a circuit getslabeled with a"+"or a"-"depends on the other point to which it is referenced.Take a look at thefollowing circuit,where each corner of the loop is marked with a number for reference:Battery-+1 2(break)no flow!no flow!-+341.4.VOLTAGE AND CURRENT xxixWith the circuit's continuity broken between points 2 and 3,the polarity of the voltage droppedbetween points 2 and 3 is"-"for point 2 and"+"for point 3.The battery's polarity (1"-"and4"+") is trying to push electrons through the loop clockwise from 1 to 2 to 3 to 4 and back to 1again.Now let's see what happens if we connect points 2 and 3 back together again,but place a breakin the circuit between points 3 and 4:Battery-+1 2(break)no flow!no flow!34-+With the break between 3 and 4,the polarity of the voltage drop between those two points is"+"for 4 and"-"for 3.Take special note of the fact that point 3's"sign"is opposite of that in the¯rst example,where the break was between points 2 and 3 (where point 3 was labeled"+").It isimpossible for us to say that point 3 in this circuit will always be either"+"or"-",because polarity,like voltage itself,is not speci¯c to a single point,but is always relative between two points!² REVIEW:² Electrons can be motivated to °ow through a conductor by the same force manifested in staticelectricity.² Voltage is the measure of speci¯c potential energy (potential energy per unit charge) betweentwo locations.In layman's terms,it is the measure of"push"available to motivate electrons.² Voltage,as an expression of potential energy,is always relative between two locations,orpoints.Sometimes it is called a voltage"drop."² When a voltage source is connected to a circuit,the voltage will cause a uniform °ow ofelectrons through that circuit called a current.² In a single (one loop) circuit,the amount of current at any point is the same as the amountof current at any other point.² If a circuit containing a voltage source is broken,the full voltage of that source will appearacross the points of the break.² The +/- orientation a voltage drop is called the polarity.It is also relative between two points.xxx CHAPTER 1.BASIC CONCEPTS OF ELECTRICITY1.5 ResistanceThe circuit in the previous section is not a very practical one.In fact,it can be quite dangerousto build (directly connecting the poles of a voltage source together with a single piece of wire).The reason it is dangerous is because the magnitude of electric current may be very large in such ashort circuit,and the release of energy very dramatic (usually in the form of heat).Usually,electriccircuits are constructed in such a way as to make practical use of that released energy,in as safe amanner as possible.One practical and popular use of electric current is for the operation of electric lighting.Thesimplest form of electric lamp is a tiny metal"¯lament"inside of a clear glass bulb,which glowswhite-hot ("incandesces") with heat energy when su±cient electric current passes through it.Likethe battery,it has two conductive connection points,one for electrons to enter and the other forelectrons to exit.Connected to a source of voltage,an electric lamp circuit looks something like this:Battery-+electron flowelectron flowElectric lamp (glowing)As the electrons work their way through the thin metal ¯lament of the lamp,they encountermore opposition to motion than they typically would in a thick piece of wire.This opposition toelectric current depends on the type of material,its cross-sectional area,and its temperature.It istechnically known as resistance.(It can be said that conductors have low resistance and insulatorshave very high resistance.) This resistance serves to limit the amount of current through the circuitwith a given amount of voltage supplied by the battery,as compared with the"short circuit"wherewe had nothing but a wire joining one end of the voltage source (battery) to the other.When electrons move against the opposition of resistance,"friction"is generated.Just likemechanical friction,the friction produced by electrons °owing against a resistance manifests itselfin the form of heat.The concentrated resistance of a lamp's ¯lament results in a relatively largeamount of heat energy dissipated at that ¯lament.This heat energy is enough to cause the ¯lamentto glow white-hot,producing light,whereas the wires connecting the lamp to the battery (whichhave much lower resistance) hardly even get warm while conducting the same amount of current.As in the case of the short circuit,if the continuity of the circuit is broken at any point,electron°ow stops throughout the entire circuit.With a lamp in place,this means that it will stop glowing:1.5.RESISTANCE xxxiBattery-+(break)no flow!no flow!no flow!- +voltagedropElectric lamp(not glowing)As before,with no °ow of electrons,the entire potential (voltage) of the battery is availableacross the break,waiting for the opportunity of a connection to bridge across that break and permitelectron °ow again.This condition is known as an open circuit,where a break in the continuity of thecircuit prevents current throughout.All it takes is a single break in continuity to"open"a circuit.Once any breaks have been connected once again and the continuity of the circuit re-established,itis known as a closed circuit.What we see here is the basis for switching lamps on and o® by remote switches.Because anybreak in a circuit's continuity results in current stopping throughout the entire circuit,we can use adevice designed to intentionally break that continuity (called a switch),mounted at any convenientlocation that we can run wires to,to control the °ow of electrons in the circuit:Battery-+switchIt doesn't matter how twisted orconvoluted a route the wires takeconducting current, so long as theyform a complete, uninterrupted loop (circuit).This is how a switch mounted on the wall of a house can control a lamp that is mounted down along hallway,or even in another room,far away from the switch.The switch itself is constructed ofa pair of conductive contacts (usually made of some kind of metal) forced together by a mechanicallever actuator or pushbutton.When the contacts touch each other,electrons are able to °ow fromone to the other and the circuit's continuity is established;when the contacts are separated,electron°ow from one to the other is prevented by the insulation of the air between,and the circuit'scontinuity is broken.Perhaps the best kind of switch to show for illustration of the basic principle is the"knife"switch:xxxii CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYA knife switch is nothing more than a conductive lever,free to pivot on a hinge,coming intophysical contact with one or more stationary contact points which are also conductive.The switchshown in the above illustration is constructed on a porcelain base (an excellent insulating material),using copper (an excellent conductor) for the"blade"and contact points.The handle is plastic toinsulate the operator's hand from the conductive blade of the switch when opening or closing it.Here is another type of knife switch,with two stationary contacts instead of one:The particular knife switch shown here has one"blade"but two stationary contacts,meaningthat it can make or break more than one circuit.For now this is not terribly important to be awareof,just the basic concept of what a switch is and how it works.Knife switches are great for illustrating the basic principle of how a switch works,but theypresent distinct safety problems when used in high-power electric circuits.The exposed conductorsin a knife switch make accidental contact with the circuit a distinct possibility,and any sparkingthat may occur between the moving blade and the stationary contact is free to ignite any nearby°ammable materials.Most modern switch designs have their moving conductors and contact pointssealed inside an insulating case in order to mitigate these hazards.A photograph of a few modern1.5.RESISTANCE xxxiiiswitch types show how the switching mechanisms are much more concealed than with the knifedesign:In keeping with the"open"and"closed"terminology of circuits,a switch that is making contactfrom one connection terminal to the other (example:a knife switch with the blade fully touchingthe stationary contact point) provides continuity for electrons to °ow through,and is called a closedswitch.Conversely,a switch that is breaking continuity (example:a knife switch with the blade nottouching the stationary contact point) won't allow electrons to pass through and is called an openswitch.This terminology is often confusing to the new student of electronics,because the words"open"and"closed"are commonly understood in the context of a door,where"open"is equatedwith free passage and"closed"with blockage.With electrical switches,these terms have oppositemeaning:"open"means no °ow while"closed"means free passage of electrons.² REVIEW:² Resistance is the measure of opposition to electric current.² A short circuit is an electric circuit o®ering little or no resistance to the °ow of electrons.Shortcircuits are dangerous with high voltage power sources because the high currents encounteredcan cause large amounts of heat energy to be released.² An open circuit is one where the continuity has been broken by an interruption in the pathfor electrons to °ow.² A closed circuit is one that is complete,with good continuity throughout.² A device designed to open or close a circuit under controlled conditions is called a switch.xxxiv CHAPTER 1.BASIC CONCEPTS OF ELECTRICITY² The terms"open"and"closed"refer to switches as well as entire circuits.An open switch isone without continuity:electrons cannot °ow through it.A closed switch is one that providesa direct (low resistance) path for electrons to °ow through.1.6 Voltage and current in a practical circuitBecause it takes energy to force electrons to °ow against the opposition of a resistance,there willbe voltage manifested (or"dropped") between any points in a circuit with resistance between them.It is important to note that although the amount of current (the quantity of electrons moving pasta given point every second) is uniform in a simple circuit,the amount of voltage (potential energyper unit charge) between di®erent sets of points in a single circuit may vary considerably:Battery-+1 234same rate of current . . .. . . at all points in this circuitTake this circuit as an example.If we label four points in this circuit with the numbers 1,2,3,and 4,we will ¯nd that the amount of current conducted through the wire between points 1 and 2is exactly the same as the amount of current conducted through the lamp (between points 2 and3).This same quantity of current passes through the wire between points 3 and 4,and through thebattery (between points 1 and 4).However,we will ¯nd the voltage appearing between any two of these points to be directlyproportional to the resistance within the conductive path between those two points,given that theamount of current along any part of the circuit's path is the same (which,for this simple circuit,itis).In a normal lamp circuit,the resistance of a lamp will be much greater than the resistance ofthe connecting wires,so we should expect to see a substantial amount of voltage between points 2and 3,with very little between points 1 and 2,or between 3 and 4.The voltage between points 1and 4,of course,will be the full amount of"force"o®ered by the battery,which will be only slightlygreater than the voltage across the lamp (between points 2 and 3).This,again,is analogous to the water reservoir system:1.7.CONVENTIONAL VERSUS ELECTRON FLOW xxxvPumpPondReservoirWaterwheel(energy released)(energy stored)1234Between points 2 and 3,where the falling water is releasing energy at the water-wheel,thereis a di®erence of pressure between the two points,re°ecting the opposition to the °ow of waterthrough the water-wheel.From point 1 to point 2,or from point 3 to point 4,where water is°owing freely through reservoirs with little opposition,there is little or no di®erence of pressure (nopotential energy).However,the rate of water °ow in this continuous system is the same everywhere(assuming the water levels in both pond and reservoir are unchanging):through the pump,throughthe water-wheel,and through all the pipes.So it is with simple electric circuits:the rate of electron°ow is the same at every point in the circuit,although voltages may di®er between di®erent sets ofpoints.1.7 Conventional versus electron °ow"The nice thing about standards is that there are so many of them to choose from."Andrew S.Tannenbaum,computer science professorWhen Benjamin Franklin made his conjecture regarding the direction of charge °ow (from thesmooth wax to the rough wool),he set a precedent for electrical notation that exists to this day,despite the fact that we know electrons are the constituent units of charge,and that they aredisplaced from the wool to the wax { not from the wax to the wool { when those two substancesare rubbed together.This is why electrons are said to have a negative charge:because Franklinassumed electric charge moved in the opposite direction that it actually does,and so objects hecalled"negative"(representing a de¯ciency of charge) actually have a surplus of electrons.By the time the true direction of electron °ow was discovered,the nomenclature of"positive"and"negative"had already been so well established in the scienti¯c community that no e®ort was madeto change it,although calling electrons"positive"would make more sense in referring to"excess"charge.You see,the terms"positive"and"negative"are human inventions,and as such have noxxxvi CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYabsolute meaning beyond our own conventions of language and scienti¯c description.Franklin couldhave just as easily referred to a surplus of charge as"black"and a de¯ciency as"white,"in which casescientists would speak of electrons having a"white"charge (assuming the same incorrect conjectureof charge position between wax and wool).However,because we tend to associate the word"positive"with"surplus"and"negative"with"de¯ciency,"the standard label for electron charge does seem backward.Because of this,manyengineers decided to retain the old concept of electricity with"positive"referring to a surplusof charge,and label charge °ow (current) accordingly.This became known as conventional °ownotation:+-Conventional flow notationElectric charge moves from the positive (surplus)side of the battery to thenegative (deficiency) side.Others chose to designate charge °ow according to the actual motion of electrons in a circuit.This form of symbology became known as electron °ow notation:+-Electric charge moves side of the battery to theElectron flow notationfrom the negative (surplus)positive (deficiency) side.In conventional °ow notation,we show the motion of charge according to the (technically incor-rect) labels of + and -.This way the labels make sense,but the direction of charge °ow is incorrect.In electron °ow notation,we follow the actual motion of electrons in the circuit,but the + and -labels seem backward.Does it matter,really,how we designate charge °ow in a circuit?Not really,so long as we're consistent in the use of our symbols.You may follow an imagined direction ofcurrent (conventional °ow) or the actual (electron °ow) with equal success insofar as circuit analysisis concerned.Concepts of voltage,current,resistance,continuity,and even mathematical treatmentssuch as Ohm's Law (chapter 2) and Kirchho®'s Laws (chapter 6) remain just as valid with eitherstyle of notation.You will ¯nd conventional °ow notation followed by most electrical engineers,and illustratedin most engineering textbooks.Electron °ow is most often seen in introductory textbooks (thisone included) and in the writings of professional scientists,especially solid-state physicists who areconcerned with the actual motion of electrons in substances.These preferences are cultural,in the1.7.CONVENTIONAL VERSUS ELECTRON FLOW xxxviisense that certain groups of people have found it advantageous to envision electric current motion incertain ways.Being that most analyses of electric circuits do not depend on a technically accuratedepiction of charge °ow,the choice between conventional °ow notation and electron °ow notationis arbitrary...almost.Many electrical devices tolerate real currents of either direction with no di®erence in operation.Incandescent lamps (the type utilizing a thin metal ¯lament that glows white-hot with su±cientcurrent),for example,produce light with equal e±ciency regardless of current direction.They evenfunction well on alternating current (AC),where the direction changes rapidly over time.Conductorsand switches operate irrespective of current direction,as well.The technical termfor this irrelevanceof charge °owis nonpolarization.We could say then,that incandescent lamps,switches,and wires arenonpolarized components.Conversely,any device that functions di®erently on currents of di®erentdirection would be called a polarized device.There are many such polarized devices used in electric circuits.Most of them are made of so-called semiconductor substances,and as such aren't examined in detail until the third volume of thisbook series.Like switches,lamps,and batteries,each of these devices is represented in a schematicdiagram by a unique symbol.As one might guess,polarized device symbols typically contain anarrow within them,somewhere,to designate a preferred or exclusive direction of current.This iswhere the competing notations of conventional and electron °ow really matter.Because engineersfrom long ago have settled on conventional °ow as their"culture's"standard notation,and becauseengineers are the same people who invent electrical devices and the symbols representing them,thearrows used in these devices'symbols all point in the direction of conventional °ow,not electron°ow.That is to say,all of these devices'symbols have arrow marks that point against the actual°ow of electrons through them.Perhaps the best example of a polarized device is the diode.A diode is a one-way"valve"forelectric current,analogous to a check valve for those familiar with plumbing and hydraulic systems.Ideally,a diode provides unimpeded °ow for current in one direction (little or no resistance),butprevents °ow in the other direction (in¯nite resistance).Its schematic symbol looks like this:DiodePlaced within a battery/lamp circuit,its operation is as such:+-Diode operationCurrent permitted+-Current prohibitedWhen the diode is facing in the proper direction to permit current,the lamp glows.Otherwise,the diode blocks all electron °ow just like a break in the circuit,and the lamp will not glow.If we label the circuit current using conventional °ow notation,the arrow symbol of the diodexxxviii CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYmakes perfect sense:the triangular arrowhead points in the direction of charge °ow,from positiveto negative:+-Current shown usingconventional flow notationOn the other hand,if we use electron °ow notation to show the true direction of electron travelaround the circuit,the diode's arrow symbology seems backward:+-Current shown usingelectron flow notationFor this reason alone,many people choose to make conventional °owtheir notation of choice whendrawing the direction of charge motion in a circuit.If for no other reason,the symbols associatedwith semiconductor components like diodes make more sense this way.However,others choose toshow the true direction of electron travel so as to avoid having to tell themselves,"just rememberthe electrons are actually moving the other way"whenever the true direction of electron motionbecomes an issue.In this series of textbooks,I have committed to using electron °ow notation.Ironically,this wasnot my ¯rst choice.I found it much easier when I was ¯rst learning electronics to use conventional°ow notation,primarily because of the directions of semiconductor device symbol arrows.Later,when I began my ¯rst formal training in electronics,my instructor insisted on using electron °ownotation in his lectures.In fact,he asked that we take our textbooks (which were illustrated usingconventional °ow notation) and use our pens to change the directions of all the current arrows soas to point the"correct"way!His preference was not arbitrary,though.In his 20-year career as aU.S.Navy electronics technician,he worked on a lot of vacuum-tube equipment.Before the adventof semiconductor components like transistors,devices known as vacuum tubes or electron tubes wereused to amplify small electrical signals.These devices work on the phenomenon of electrons hurtlingthrough a vacuum,their rate of °ow controlled by voltages applied between metal plates and gridsplaced within their path,and are best understood when visualized using electron °ow notation.When I graduated from that training program,I went back to my old habit of conventional °ow1.8.CONTRIBUTORS xxxixnotation,primarily for the sake of minimizing confusion with component symbols,since vacuumtubes are all but obsolete except in special applications.Collecting notes for the writing of thisbook,I had full intention of illustrating it using conventional °ow.Years later,when I became a teacher of electronics,the curriculum for the program I was goingto teach had already been established around the notation of electron °ow.Oddly enough,thiswas due in part to the legacy of my ¯rst electronics instructor (the 20-year Navy veteran),butthat's another story entirely!Not wanting to confuse students by teaching"di®erently"from theother instructors,I had to overcome my habit and get used to visualizing electron °ow instead ofconventional.Because I wanted my book to be a useful resource for my students,I begrudginglychanged plans and illustrated it with all the arrows pointing the"correct"way.Oh well,sometimesyou just can't win!On a positive note (no pun intended),I have subsequently discovered that some students preferelectron °ow notation when ¯rst learning about the behavior of semiconductive substances.Also,the habit of visualizing electrons °owing against the arrows of polarized device symbols isn't thatdi±cult to learn,and in the end I've found that I can follow the operation of a circuit equally wellusing either mode of notation.Still,I sometimes wonder if it would all be much easier if we wentback to the source of the confusion { Ben Franklin's errant conjecture { and ¯xed the problem there,calling electrons"positive"and protons"negative."1.8 ContributorsContributors to this chapter are listed in chronological order of their contributions,frommost recentto ¯rst.See Appendix 2 (Contributor List) for dates and contact information.Bill Heath (September 2002):Pointed out error in illustration of carbon atom { the nucleuswas shown with seven protons instead of six.Stefan Kluehspies (June 2003):Corrected spelling error in Andrew Tannenbaum's name.Ben Crowell,Ph.D.(January 13,2001):suggestions on improving the technical accuracy ofvoltage and charge de¯nitions.Jason Starck (June 2000):HTML document formatting,which led to a much better-lookingsecond edition.xl CHAPTER 1.BASIC CONCEPTS OF ELECTRICITYChapter 2OHM's LAWContents2.1 How voltage,current,and resistance relate...............xli2.2 An analogy for Ohm's Law.........................xlvi2.3 Power in electric circuits..........................xlvii2.4 Calculating electric power..........................xlix2.5 Resistors....................................lii2.6 Nonlinear conduction............................lvii2.7 Circuit wiring.................................lxii2.8 Polarity of voltage drops..........................lxvi2.9 Computer simulation of electric circuits.................lxvii2.10 Contributors..................................lxxxi"One microampere °owing in one ohm causes a one microvolt potential drop."Georg Simon Ohm2.1 How voltage,current,and resistance relateAn electric circuit is formed when a conductive path is created to allow free electrons to continuouslymove.This continuous movement of free electrons through the conductors of a circuit is called acurrent,and it is often referred to in terms of"°ow,"just like the °ow of a liquid through a hollowpipe.The force motivating electrons to"°ow"in a circuit is called voltage.Voltage is a speci¯c measureof potential energy that is always relative between two points.When we speak of a certain amountof voltage being present in a circuit,we are referring to the measurement of how much potentialenergy exists to move electrons from one particular point in that circuit to another particular point.Without reference to two particular points,the term"voltage"has no meaning.Free electrons tend to move through conductors with some degree of friction,or opposition tomotion.This opposition to motion is more properly called resistance.The amount of current in axlixlii CHAPTER 2.OHM'S LAWcircuit depends on the amount of voltage available to motivate the electrons,and also the amountof resistance in the circuit to oppose electron °ow.Just like voltage,resistance is a quantity relativebetween two points.For this reason,the quantities of voltage and resistance are often stated asbeing"between"or"across"two points in a circuit.To be able to make meaningful statements about these quantities in circuits,we need to be ableto describe their quantities in the same way that we might quantify mass,temperature,volume,length,or any other kind of physical quantity.For mass we might use the units of"pound"or"gram."For temperature we might use degrees Fahrenheit or degrees Celsius.Here are the standardunits of measurement for electrical current,voltage,and resistance:Quantity SymbolMeasurementUnit ofAbbreviationUnitCurrentVoltageResistanceIE VorRAmpere ("Amp")VoltOhmAVThe"symbol"given for each quantity is the standard alphabetical letter used to represent thatquantity in an algebraic equation.Standardized letters like these are common in the disciplinesof physics and engineering,and are internationally recognized.The"unit abbreviation"for eachquantity represents the alphabetical symbol used as a shorthand notation for its particular unit ofmeasurement.And,yes,that strange-looking"horseshoe"symbol is the capital Greek letter ­,justa character in a foreign alphabet (apologies to any Greek readers here).Each unit of measurement is named after a famous experimenter in electricity:The amp afterthe Frenchman Andre M.Ampere,the volt after the Italian Alessandro Volta,and the ohm afterthe German Georg Simon Ohm.The mathematical symbol for each quantity is meaningful as well.The"R"for resistance andthe"V"for voltage are both self-explanatory,whereas"I"for current seems a bit weird.The"I"is thought to have been meant to represent"Intensity"(of electron °ow),and the other symbol forvoltage,"E,"stands for"Electromotive force."From what research I've been able to do,there seemsto be some dispute over the meaning of"I."The symbols"E"and"V"are interchangeable for themost part,although some texts reserve"E"to represent voltage across a source (such as a batteryor generator) and"V"to represent voltage across anything else.All of these symbols are expressed using capital letters,except in cases where a quantity (espe-cially voltage or current) is described in terms of a brief period of time (called an"instantaneous"value).For example,the voltage of a battery,which is stable over a long period of time,will besymbolized with a capital letter"E,"while the voltage peak of a lightning strike at the very instantit hits a power line would most likely be symbolized with a lower-case letter"e"(or lower-case"v")to designate that value as being at a single moment in time.This same lower-case convention holdstrue for current as well,the lower-case letter"i"representing current at some instant in time.Mostdirect-current (DC) measurements,however,being stable over time,will be symbolized with capitalletters.One foundational unit of electrical measurement,often taught in the beginnings of electronicscourses but used infrequently afterwards,is the unit of the coulomb,which is a measure of electriccharge proportional to the number of electrons in an imbalanced state.One coulomb of charge is2.1.HOWVOLTAGE,CURRENT,AND RESISTANCE RELATE xliiiequal to 6,250,000,000,000,000,000 electrons.The symbol for electric charge quantity is the capitalletter"Q,"with the unit of coulombs abbreviated by the capital letter"C."It so happens that theunit for electron °ow,the amp,is equal to 1 coulomb of electrons passing by a given point in acircuit in 1 second of time.Cast in these terms,current is the rate of electric charge motion througha conductor.As stated before,voltage is the measure of potential energy per unit charge available to motivateelectrons from one point to another.Before we can precisely de¯ne what a"volt"is,we mustunderstand how to measure this quantity we call"potential energy."The general metric unit forenergy of any kind is the joule,equal to the amount of work performed by a force of 1 newtonexerted through a motion of 1 meter (in the same direction).In British units,this is slightly lessthan 3/4 pound of force exerted over a distance of 1 foot.Put in common terms,it takes about 1joule of energy to lift a 3/4 pound weight 1 foot o® the ground,or to drag something a distance of1 foot using a parallel pulling force of 3/4 pound.De¯ned in these scienti¯c terms,1 volt is equalto 1 joule of electric potential energy per (divided by) 1 coulomb of charge.Thus,a 9 volt batteryreleases 9 joules of energy for every coulomb of electrons moved through a circuit.These units and symbols for electrical quantities will become very important to know as webegin to explore the relationships between them in circuits.The ¯rst,and perhaps most important,relationship between current,voltage,and resistance is called Ohm's Law,discovered by GeorgSimon Ohm and published in his 1827 paper,The Galvanic Circuit Investigated Mathematically.Ohm's principal discovery was that the amount of electric current through a metal conductor ina circuit is directly proportional to the voltage impressed across it,for any given temperature.Ohm expressed his discovery in the form of a simple equation,describing how voltage,current,andresistance interrelate:E = I RIn this algebraic expression,voltage (E) is equal to current (I) multiplied by resistance (R).Usingalgebra techniques,we can manipulate this equation into two variations,solving for I and for R,respectively:I =ERR =EILet's see how these equations might work to help us analyze simple circuits:Battery-+electron flowelectron flowElectric lamp (glowing)In the above circuit,there is only one source of voltage (the battery,on the left) and only onexliv CHAPTER 2.OHM'S LAWsource of resistance to current (the lamp,on the right).This makes it very easy to apply Ohm'sLaw.If we know the values of any two of the three quantities (voltage,current,and resistance) inthis circuit,we can use Ohm's Law to determine the third.In this ¯rst example,we will calculate the amount of current (I) in a circuit,given values ofvoltage (E) and resistance (R):Battery-+LampE = 12 VI = ???I = ???R = 3 What is the amount of current (I) in this circuit?I =ER==12 V3 4 AIn this second example,we will calculate the amount of resistance (R) in a circuit,given valuesof voltage (E) and current (I):Battery-+LampE = 36 VI = 4 AI = 4 AR = ???What is the amount of resistance (R) o®ered by the lamp?ER===I36 V4 A9 In the last example,we will calculate the amount of voltage supplied by a battery,given valuesof current (I) and resistance (R):2.1.HOWVOLTAGE,CURRENT,AND RESISTANCE RELATE xlvBattery-+LampE = ???I = 2 AI = 2 AR = 7 What is the amount of voltage provided by the battery?R =IE = (2 A)(7  ) = 14 VOhm's Law is a very simple and useful tool for analyzing electric circuits.It is used so oftenin the study of electricity and electronics that it needs to be committed to memory by the seriousstudent.For those who are not yet comfortable with algebra,there's a trick to remembering how tosolve for any one quantity,given the other two.First,arrange the letters E,I,and R in a trianglelike this:EI RIf you know E and I,and wish to determine R,just eliminate R from the picture and see what'sleft:EI REIR =If you know E and R,and wish to determine I,eliminate I and see what's left:EI REI =RLastly,if you know I and R,and wish to determine E,eliminate E and see what's left:xlvi CHAPTER 2.OHM'S LAWEI RE = I REventually,you'll have to be familiar with algebra to seriously study electricity and electronics,but this tip can make your ¯rst calculations a little easier to remember.If you are comfortable withalgebra,all you need to do is commit E=IR to memory and derive the other two formulae from thatwhen you need them!² REVIEW:² Voltage measured in volts,symbolized by the letters"E"or"V".² Current measured in amps,symbolized by the letter"I".² Resistance measured in ohms,symbolized by the letter"R".² Ohm's Law:E = IR;I = E/R;R = E/I2.2 An analogy for Ohm's LawOhm's Law also makes intuitive sense if you apply it to the water-and-pipe analogy.If we havea water pump that exerts pressure (voltage) to push water around a"circuit"(current) through arestriction (resistance),we can model how the three variables interrelate.If the resistance to water°ow stays the same and the pump pressure increases,the °ow rate must also increase.PressureFlow rateResistance===VoltageCurrentResistance===increasesameincrease increaseincreasesameE = I RIf the pressure stays the same and the resistance increases (making it more di±cult for the water